Question

4. Davy Metal Company produces brass fitings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. 500L0.6K0.8, where Q- annual output measured in pounds, L - labor measured in person hours, K -capital measured in machine hours. The marginal products of labor and capital are therefore MPL-300L-0.4K0.8 MPK-400L0.6K-0.2 Davy's employees are relatively highly skilled, so labour costs 15 per hour. The firm estimates a rental charge of є50 per hour on capital. Davy forecasts an annual budget (annual costs) of€500.000 per year, measured in real dollars. (a) What is an isocost line? Draw the isocost line for Davy Metal for the budget of €500,000. (b) Determine the appropriate input mix of K and L to get the maximum output for an outlay of€500,000 for a production run of brass fittings. Compute Q, the maximum output. Illustrate this on a graph

Answer 1

labor cost (w) = 615 per hour rental charge of capital (r);= elementof 50 .per hour annual cost (budget) = epsilon 500000. In cost line equation: wL + r K = cost 15 L + 50 = 500000 rightarrow (1) for y - axis intercept of line put L = 0 rightarrow 15 (0) + 50 K = 500000 50 k = 500000/ 50 k = 10000 For x - axis intercept of is cost line, put k = 0 rightarrow 15 L + 50 (0) = 500000 15 L = 500000 L = 33333 \r\n b) sol mo_L/mp_k = w/r to optimize the production rightarrow 300 L^-0.4 k^0.8/400 L^0.6 k^-.0.2 = 15/50 300 /400 k^0.8/L^0.6 k^0.2/L^0.4 = 15/50 300/ 400 K/L = 15/50 rightarrow K/L = (15/50) (400/300) rightarrow K/L = 6000/15000 rightarrow K/L = 0.4 rightarrow K = 0.4 L rightarrow (2) substitute (2) in (1) 15L + 50 K = 50000015 L + 50 (0.4L) = 500000 15 L + 20 L = 500000 35 L = 5000000 L = 500000/35 L = 14286 and k = 0.4 (500000/35) rightarrow k = 200000/35